266 



Fishery Bulletin 98(2) 



300- 



200- 



t: 

 o 



c 



£ 100- 



O 

 CO 



ter probability. Only the north— south direction was 

 relevant because the transect was run from east 

 to west. Similarly, schools were randomly allocated 

 within a school group and when schools overlapped 

 in the north-south direction, they were combined as 

 a "single" school for computing purposes. This pro- 

 cess continued until all schools were separated in the 

 north-south direction and termed "disjoint" schools. 

 The distance (gaps) between disjoint schools in the 

 north-south direction were summed for each school 

 group and later summed for all fish groups. The sum 

 of n-s gaps within school groups was termed "total 

 gap within." Similarly, a "total gap between" (dis- 

 joint school groups) was also computed. Both "total 

 gap within" and "total gap between" were used to 

 compute the encounter probability ip^,) (the probabil- 

 ity that at least one fish school is detected): 



p^ = I - (total gap within + total gap between)/L 



or 





n~\ 



vn- 



Z<G, 



y) + E 



(1) 



Py 



where v = the swath width in meter; 



gj = the gap length between/*^ andj'+l'^ dis- 

 joint school within a school 

 group and the quantity of 



o 



TT 



XT 



o 



o 



o 



150 



T 



1^ 

 50 



Gl 

 G2 

 G3 



100 



East-west direction (km 



Figure 1 



A spatial distribution of school groups from one simulation run. Circles indicate areas 

 covered by school groups for a population of 80,000 schools. This graph was generated 

 from lognormal distributions with mean = 3.91 and variance = 0.51 for school density 

 (number of schools/nmi'-i and from lognormal distribution with mean = 2.319 and vari- 

 ance = 0.676 for diameter (nmii of school group (nmi was later converted to km I. Gl, 

 G2, G3, and E are the gaps used to compute the encounter probability (Eq. 1 1. 



g„ - y is set to zero if ^^^ is 



G, 



th 



N = 



less than v; 



the gap length between 7 

 and i+V^ disjoint school 

 groups and G, - 3' is set to 

 zero if G, is less than y; 

 the distance between the 

 north and south end of the 

 survey area and their near- 

 est anchovy schools; 

 number of school groups 

 disjoint in the north-south 

 direction; and 

 333 km ( 180 nautical miles 

 [nmi]) which is about the 

 length of the coastline along 

 the Southern California 

 Bight. 



Smith (1981) reported that the 

 diameter (nmi) of a school group 

 followed a lognormal distribution 

 and had a logarithmic mean of 

 2.319 and a logarithmic variance 



